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On the One-Way Function Candidate Proposed by Goldreich

James Cook, Omid Etesami, Rachel Miller, Luca Trevisan
2014 ACM Transactions on Computation Theory  
Goldreich [2000] proposed a candidate one-way function based on a bipartite graph of small right-degree d, where the vertices on the left (resp. right) represent input (resp. output) bits of the function  ...  Inverting this function as a one-way function by definition means finding an element in the preimage of output of this function for a random input. We bound the expected size of this preimage.  ...  INTRODUCTION Goldreich [2000] proposed a candidate one-way function based on expanders.  ... 
doi:10.1145/2633602 fatcat:h5t477pcxnefxpmyyzvyvjgo5q

Page 10251 of Mathematical Reviews Vol. , Issue 2004m [page]

2004 Mathematical Reviews  
We propose two natural candidate quantum Yao principles, a ‘weak’ and a ‘strong’ one.  ...  If the one-way function acts on n-bit strings then the overhead in the reduction is by a factor of O(n/e*) in the classical case but only by a factor of O(1/e) in the quantum case, where 4+ is the probability  ... 

The Complexity of Public-Key Cryptography [chapter]

Boaz Barak
2017 Tutorials on the Foundations of Cryptography  
We discuss the computational assumptions that have been used as bases for public-key encryption schemes, and the types of evidence we have for the veracity of these assumptions.  ...  We survey the computational foundations for public-key cryptography.  ...  Thus, if this algorithm cannot be improved to work in an optimal number of samples and polynomial time, then one-way functions exist. 10 Goldreich's One-Way Function Candidate Goldreich has proposed  ... 
doi:10.1007/978-3-319-57048-8_2 fatcat:74ecqky6sraifpvfnylqxc6jom

Text Encryption using Lattice-Based Cryptography

Vishnu Kumar
2014 IOSR Journal of Computer Engineering  
There are strong indications that these problems will remain secure under the assumption of the availability of quantum computers, unlike both the integer-factorization and discrete logarithm problems  ...  In this paper, the author will explore various methods to improve the practicality of lattice-based cryptosystems (GGH Encryption scheme) and to optimize the algorithm that make up these cryptosystems  ...  The Goldreich-Goldwasser-Halevi (GGH) cryptosystem makes use of the fact that the closest vector problem can be a hard problem.It uses a trapdoor one-way function that is relying on the difficulty of lattice  ... 
doi:10.9790/0661-1628148151 fatcat:3rj53rojr5ek7h3syfc2kc6cxu

Concentration of the number of solutions of random planted CSPs and Goldreich's one-way candidates [article]

Emmanuel Abbe, Katherine Edwards
2015 arXiv   pre-print
The result is also extended to a more general class of random planted CSPs; in particular, it is shown that the number of pre-images for the Goldreich one-way function model concentrates for some choices  ...  Specifically, if F^*_k(α,n) is a random k-SAT formula on n variables, with clause density α and with a uniformly drawn planted solution, there exists a function ϕ_k(·) such that, besides for some α in  ...  Impagliazzo for suggesting the Goldreich one-way function model to the first author, as well as A. Montanari for stimulating discussions.  ... 
arXiv:1504.08316v1 fatcat:fjrnsb4ajvhmzmcjije64yc27a

A Candidate Counterexample to the Easy Cylinders Conjecture [chapter]

Oded Goldreich
2011 Lecture Notes in Computer Science  
Our suggestion builds on the candidate one-way function based on expander graphs (see ECCC, TR00-090), and essentially consists of iterating this function polynomially many times.  ...  We present a candidate counterexample to the easy cylinders conjecture, which was recently suggested by Manindra Agrawal and Osamu Watanabe (see ECCC, TR09-019).  ...  Agrawal and Watanabe noted that all popular candidates one-way functions have easy cylinders.  ... 
doi:10.1007/978-3-642-22670-0_16 fatcat:yfthdakkcvgsbdpkvzbuulunbu

Candidate One-Way Functions and One-Way Permutations Based on Quasigroup String Transformations [article]

Danilo Gligoroski
2005 arXiv   pre-print
In this paper we propose a definition and construction of a new family of one-way candidate functions R_N:Q^N → Q^N, where Q={0,1,...,s-1} is an alphabet with s elements.  ...  table that defines them (a Latin Square) in order to check the satisfiability for the initial conditions, thus making them natural candidates for one-way functions.  ...  There are also some one-way functions candidates based on sphere-packing problems and coding theory such as the proposals from Goldreich, Krawczyk and Luby in [4] .  ... 
arXiv:cs/0510018v1 fatcat:gjczxwmsc5d53ompvopnjcss4q

One Way Functions –Conjecture, Status, Applications and Future Research Scope

Amit Sharma, Sunil Kr.
2016 International Journal of Computer Applications  
This paper presents the features and limitations of proposed candidate functions, and the implications of proof of one way functions conjecture.  ...  The conjecture that one way function exists is an open problem, the resolution of which holds the key for the solution of many unsolved problems in mathematics and cryptography.  ...  Over the years, various candidate functions have been proposed as one way functions, which have withstand the rigorous cryptanalysis tests and extensive research for finding their inverse and have been  ... 
doi:10.5120/ijca2016912126 fatcat:jttkqoy3ercupctqpyqmtyphsu

Paillier's trapdoor function hides Θ(n) bits

Dong Su, KeWei Lü
2011 Science China Information Sciences  
In this paper, we re-examine the bit security of Paillier's trapdoor function.  ...  For the simultaneous security, we prove that n number of the class c's bits are simultaneously hard-core under the standard assumption, where n is the length of c.  ...  Acknowledgements This work is partially supported by the National Natural Science Foundation of China (Grant No. 60970154), and the National Basic Research Program of China (Grant No. 2007CB311202).  ... 
doi:10.1007/s11432-011-4269-9 fatcat:6hjigkssefhydaak22trdtp2ai

Query Complexity and Error Tolerance of Witness Finding Algorithms [article]

Akinori Kawachi, Benjamin Rossman, Osamu Watanabe
2012 Electronic colloquium on computational complexity  
We propose an abstract framework for studying search-to-decision reductions for NP.  ...  Specifically, we study the following witness finding problem: for a hidden nonempty set W ⊆ {0, 1} n , the goal is to output a witness in W with constant probability by making randomized queries of the  ...  AK was supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (B) No.21300002.  ... 
dblp:journals/eccc/KawachiRW12 fatcat:qelcfhdzgzbatibowj3ktftt6y

On a Family of Minimal Candidate One-way Functions and One-way Permutations

Danilo Gligoroski
2009 International Journal of Network Security  
In this paper we propose a definition and construction of a new family of one-way candidate functions R N : Q N → Q N , where Q = {0, 1, . . . , s − 1} is an alphabet with s elements.  ...  In order to achieve computational workload equivalent to the exhaustive key search of an n-bit key for inversion of RSA or Diffie-Hellman one-way candidate functions the length of their arguments have  ...  There are also some one-way functions candidates based on sphere-packing problems and coding theory such as the proposals from Goldreich, Krawczyk and Luby in [5] .  ... 
dblp:journals/ijnsec/Gligoroski09 fatcat:aodljg6jkfhehll2rt7kg56qei

Some facets of complexity theory and cryptography: A five-lecture tutorial

Jörg Rothe
2002 ACM Computing Surveys  
A function is one-way if it is easy to compute, but hard to invert. We discuss the notion of one-way functions both in a cryptographic and in a complexity-theoretic setting.  ...  Particular attention is paid to cryptographic protocols and the problem of constructing key components of protocols such as one-way functions.  ...  I thank Kari Pasanen for being a great tutor of this tutorial, for carefully proofreading a preliminary draft of this article, and in particular for subletting his summer house on an island of scenic Lake  ... 
doi:10.1145/592642.592646 fatcat:qogelhnxlzerhmyeru6q3xcioa

Chosen ciphertext attacks on lattice-based public key encryption and modern (non-quantum) cryptography in a quantum environment

Oleg Izmerly, Tal Mor
2006 Theoretical Computer Science  
Modern cryptography is based on various building blocks such as one way functions with or without trapdoors, pseudo-random functions, one way permutations with or without trapdoors, etc.  ...  About half a decade agoAjtai and Dwork (and later on, also Goldreich, Goldwasser and Halevi) proposed a public key cryptosystem that has a proven security under a plausible complexity assumption.  ...  This work was supported in part by the Israel MOD Research and Technology Unit.  ... 
doi:10.1016/j.tcs.2006.07.060 fatcat:7fd2bjvqorgmhmacoiyjoxjqoy

Simpler Session-Key Generation from Short Random Passwords [chapter]

Minh-Huyen Nguyen, Salil Vadhan
2004 Lecture Notes in Computer Science  
The security bound achieved by our protocol is somewhat worse than the GL protocol.  ...  We present a simplification of the Goldreich-Lindell (GL) protocol and analysis for the special case when the dictionary is of the form D = {0, 1} d , i.e. the password is a short random string (like an  ...  We are also grateful to Mihir Bellare for pointing out the extension of our protocol to arbitrary dictionaries in the common random string model.  ... 
doi:10.1007/978-3-540-24638-1_24 fatcat:qh2e67zrpnh6rpd57vy5sxppv4

Goldreich's One-Way Function Candidate and Myopic Backtracking Algorithms [chapter]

James Cook, Omid Etesami, Rachel Miller, Luca Trevisan
2009 Lecture Notes in Computer Science  
Goldreich (ECCC 2000) proposed a candidate one-way function construction which is parameterized by the choice of a small predicate (over d = O(1) variables) and of a bipartite expanding graph of right-degree  ...  The function is computed by labeling the n vertices on the left with the bits of the input, labeling each of the n vertices on the right with the value of the predicate applied to the neighbors, and outputting  ...  The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-3-642-00457-5_36  ... 
doi:10.1007/978-3-642-00457-5_31 fatcat:dgt7q2r5ufgt5cpyuyrwnvkozm
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